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Corollary vs. correlation

In modern English, a corollary is an obvious deduction, a natural consequence, or a proposition that follows with little or no proof from one already proven. The word usually takes the preposition to, though of and from also workA correlation is a complementary or parallel relationship between two things, not necessarily involving causation or a direct relationship. It usually takes the preposition between. So a corollary involves one thing springing from another, while a correlation involves two things that relate to each other in some reciprocal way.

Examples

In each of these examples, the corollary is an obvious result of or conclusion from something else:


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He argues that the right of biological parents to keep and raise the child they produce is a corollary of a more general right, which is, to be allowed to finish what one has begun. [Metapsychology]

It’s ingrained in the culture; there is no shame or stigma attached to failure because it’s seen as the necessary corollary of risk-taking. [Irish Times]

As all written words consist of letters, it is an undeniable corollary from the preceding premises, that all written words are formed of the written signs of spoken sounds. [The Gentleman’s Magazine (1837)]

And in each of these examples, the correlation involves a reciprocal relationship between two things:

Despite traditional negative correlation, gold and USD has been moving in tandem since the outbreak of the anti-government unrest in Egypt. [International Business Times]

Never mind that there’s no correlation between state fiscal health and whether public employees can unionize. [Harvard Crimson]

Prepositions thus exhibit a wonderful correlation between the intellectual and physical worlds ; a correlation which shows that both worlds proceeded from the same Author. [English Grammar, William Chauncey Fowler (1850)]

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